Hi, NervousNell. As requested, here's the policy director weighing in. :-)
In the U.S., we have a system of "dual sovereignty." The federal government is one sovereign, and the individual states are each sovereigns as well. Accordingly, people standing on U.S. soil are simultaneously subjects of two different sovereigns: the federal government, and the state within which he or she is standing.
Each sovereign gets to create its own laws. States can create laws on the same subjects that Congress makes laws, and the states' laws can differ from the feds' - as long as they don't run afoul of the Supremacy Clause of the United States Constitution. The Supremacy Clause, which is Article VI, Clause 2, says, "This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby; any Thing in the Constitution or Laws of any State to the Contrary notwithstanding." This last phrase, "any Thing in the ... Laws of any State to the Contrary notwithstanding" means state laws can't conflict with federal laws that address the same topic. This is the source of the "federal preemption" doctrine that says that federal laws preempt - or, trump - state laws whenever the two conflict.
In the context of drug laws, we have even more guidance. The federal Controlled Substances Act contains its own preemption provision, 21 U.S.C. sec. 903. That provision says, "No provision of this subchapter shall be construed as indicating an intent on the part of the Congress to occupy the field in which that provision operates, including criminal penalties, to the exclusion of any State law on the same subject matter which would otherwise be within the authority of the State, unless there is a positive conflict between that provision of this subchapter and that State law so that the two cannot consistently stand together." In other words, states can create laws about marijuana that are different than the federal law as long as they do not create a "positive conflict."
What's a "positive conflict"? In County of San Diego v. San Diego NORML, et al., the California Court of Appeals explained that a state marijuana law creates a positive conflict with the federal Controlled Substances Act only when the state law affirmatively requires someone to perform an act that would be a violation of the federal marijuana prohibition. For example, if Washington were to pass a law that required every farmer to grow at least one acre of marijuana, that law would be subject to federal preemption under 21 U.S.C. sec. 903. Washington law can't require someone to break federal law.
But that doesn't mean Washington can't make marijuana legal under state law. Washington has a Uniform Controlled Substances Act that is roughly parallel to the federal Controlled Substances Act. The federal provision that prohibits marijuana possession is 21 U.S.C. sec. 844; the Washington provision is RCW 69.50.4013. Washington could amend RCW 69.50.4013 to exclude marijuana, so that someone who possessed marijuana wouldn't be breaking state law. This wouldn't mean that anyone would be required to possess marijuana, just that possession wouldn't violate state law.
This would protect somone possessing marijuana in Washington from being prosecuted under state law, but it wouldn't provide protection from prosecution under the federal law. However, the practical reality is that the federal government doesn't waste resources on small-scale marijuana offenses. Thirteen states already have laws providing that possession of a small amount of marijuana is not a crime.
So, Washington can make marijuana possession legal under state law simply by removing that offense from the state Uniform Controlled Substances Act. That wouldn't pose any federal preemption problems. The more interesting question, though, is what would happen if Washington decided to bring marijuana production and distribution under a regulatory system - in a manner similar to alcohol, for example. Such a system would most likely require someone to break federal law (depositing sales tax in a bank would constitute money laundering, for example) and therefore be vulnerable to a federal preemption challenge. But how would the political landscape change? Might a state's expression of its willingness to try something different from our failed experiment with marijuana prohibition catalyze change at the federal level?